On spin \(L\)-functions for orthogonal groups
Let \(G= GSO_{2n}\) over a number field. The dual group is \(G\text{Spin}_{2n} (\mathbb{C})\). Let \(r_n\) be the \(2^{n-1}\)-dimensional spin representation of this group. The analytic properties of the partial \(L\)- function \(L_S (\pi\otimes \chi, r_n)\) for \(\pi\) a generic cuspidal representation of \(G(\mathbb{A})\) are studied, using the Rankin-Selberg method, for \(n=5\) and \(n=6\) (these are the only cases in which the algebra of \(U\)-invariants in \(\mathbb{C} [V]\), \(V\)= space of \(r_n\), is a polynomial ring). For \(n=5\) the Rankin-Selberg integral is of Hecke type, for \(n=6\) it involves an Eisenstein series of \(GSp_6\).
scientific article; zbMATH DE number 784720
scientific article